Chooser options

For a chooser option, it allows the option buyer to choose, at a predetermined point of time before the option matures whether it is a European call or a European put. For a simple chooser option, the underlying call and put options have the same maturities and exercise prices. Let's look at two extreme cases. The option buyer has to make a decision today, that is, when they make such a purchase. The price of this chooser option should be the maximum of call and put options since the option buyer does not have more information. The second extreme case is the investor could make a decision on the maturity date. Since the call and put have the same exercise prices, if the call is in the money, the put should be out of money. The opposite is true. Thus, the price of a chooser option should be the summation of the call and the put. This is equivalent to buy a call and a put with the same exercise prices and maturity dates. In Chapter 10, Options and Futures we know such...